20,512 research outputs found

    A non-local vector calculus,non-local volume-constrained problems,and non-local balance laws

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    A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoints operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The nonlocal calculus gives rise to volume-constrained problems that are analogous to elliptic boundary-value problems for differential operators; this is demonstrated via some examples. Another application is posing abstract nonlocal balance laws and deriving the corresponding nonlocal field equations

    Microwave photoresistance of a high-mobility two-dimensional electron gas in a triangular antidot lattice

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    The microwave (MW) photoresistance has been measured on a high-mobility two-dimensional electron gas patterned with a shallow triangular antidot lattice, where both the MW-induced resistance oscillations (MIRO) and magnetoplasmon (MP) resonance are observed superposing on sharp commensurate geometrical resonance (GR). Analysis shows that the MIRO, MP, and GR are decoupled from each other in these experiments.Comment: 5 pages, 4 figures, paper accepted by PR

    Sustainable leaching process of phosphates from animal bones to alleviate the world phosphate crisis

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    Lack of available phosphorus (P) minerals and their very localized regional distribution threatens world food production. Traditional farming methods that recycle various biological wastes and manure for localized fertilization of farmland are our role model, but come with risks such as hygiene, water toxification and passed-on diseases. Here, we present a bran-new hydrothermal process which turns animal bones of kitchen wastes into secondary P sources for fertilization, showing that this hydrothermal humification (HTH) process under 200 °C for 24 h completely disintegrates chemical structure of the biomass, while the simultaneously in-situ prepared artificial humic acid (A-HA) etches even macroscopic bones. Notably, A-HA can solubilize the insoluble P existing in animal bones partly as directly dissolved phosphorus (DP), accounting for 6.36 % of total phosphorus (TP) in the bone wastes. Characterization methods indicate that oxygen-containing functional groups (i.e., -COOH and phenolic-OH) of A-HA can help to corrode bones, causing Ca5(PO4)3(OH) to be decomposed into a large number of more active P minerals, furthermore, leading to high DP (96.79 mg/L) content and the formation of new P-based species. Pot planting experiments show that the resulting liquids were applied as a fertilizer and lead to a significant promotion of the growth of seedlings

    Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity

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    How to draw the vertices of a complete multipartite graph GG on different points of a bounded dd-dimensional integer grid, such that the sum of squared distances between vertices of GG is (i) minimized or (ii) maximized? For both problems we provide a characterization of the solutions. For the particular case d=1d=1, our solution for (i) also settles the minimum-2-sum problem for complete bipartite graphs; the minimum-2-sum problem was defined by Juvan and Mohar in 1992. Weighted centroidal Voronoi tessellations are the solution for (ii). Such drawings are related with Laplacian eigenvalues of graphs. This motivates us to study which properties of the algebraic connectivity of graphs carry over to the restricted setting of drawings of graphs with integer coordinates.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

    Formation of robust and completely tunable resonant photonic band gaps

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    We identify different types of the photonic band gaps (PBGs) of two dimensional magnetic photonic crystals (MPCs) consisting of arrays of magnetic cylinders and study the different tunability (by an external static magnetic field) of these PBGs. One type of the band gaps comes from infinitely degenerate flat bands and is closely related to those in the study of plasmonics. In addition, such PBGs are magnetically tunable and robust against position disorder. We calcualte the transmission of the PBG's and found excellent agreement with the results of the photonic band structure calculation. Positional disorder of the lattice structure affects the different types of PBGs differently.Comment: 4 pages, 5 figure
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